Pumping stations deliver oil at the rate modeled by the function d, given by d of t equals the quotient of 5 times t and the quantity 1 plus 3 times t with t measure in hours and and d(t) measured in gallons per hour. how much oil will the pumping stations deliver during the 4-hour period from t = 0 to t = 4? give 3 decimal places.

The answer is:  There is a total of 5.797 gallons pumped during the given period.

To solve this equation, we need to integrate the function at the given period (from t=0 to t=4)

The given function is:

So, the integral will be:

So, integrating we have:

Performing a change of variable, we have:

Then, substituting, we have:

Reverting the change of variable, we have:

Then, evaluating we have:

So, there is a total of 5.797 gallons pumped during the given period.

Have a nice day!

dwe

step-by-step explanation:

ewd

for this case we have that by definition, the surface area of a cylinder is given by:

where:

r: it is the radius of the cylinder

h: it is the height of the cylinder

we can also rewrite it as:

where:

la: it's the lateral area

ba: area of the base

option a